System and Method for Analyzing Wellbore Survey Data to Determine Tortuosity of the Wellbore Using Displacements of the Wellbore Path from Reference Lines

ABSTRACT

A system and method for providing information regarding the tortuosity of a wellbore path is provided. The method includes receiving data from a plurality of survey stations of a wellbore survey. The method further includes defining a plurality of reference lines for the wellbore path. The method further includes determining a plurality of displacements of the wellbore path from the plurality of reference lines.

CLAIM OF PRIORITY

This application is a Continuation of patent application Ser. No.14/612162 filed Feb. 2, 2015, which claims the benefit of and priorityto Provisional Patent Application Number U.S. 62/085035, filed Nov. 26,2014; Provisional Patent Application Number U.S. 62/050019, filed Sep.12, 2014; and Provisional Patent Application Number U.S. 61/943205,filed Feb. 21, 2014, each of which is incorporated in their entirety byreference herein. This application is also generally related to patentapplication Ser. No. 14/612168, filed on Feb. 2, 2015 and titled SYSTEMAND METHOD FOR ANALYZING WELLBORE SURVEY DATA TO DETERMINE TORTUOSITY OFTHE WELLBORE USING TORTUOSITY PARAMETER VALUES which also claims thebenefit of priority to these US provisional patent applications.

BACKGROUND Field

This application relates generally to analysis of wellbore survey dataand more particularly, to systems and methods for determining atortuosity of a portion of the wellbore by analyzing the wellbore surveydata.

Description of the Related Art

The deviation of a wellbore path or trajectory from a smooth curve(e.g., the predetermined plan for the wellbore path) is commonlyreferred to as tortuosity of the wellbore path. Large variations of thewellbore path over short distances (e.g., 10 to 30 meters) in a portionof the wellbore can give rise to problems in setting casings in theportion of the wellbore, passing casings through the portion of thewellbore, in the installation of production equipment (e.g., electricsubmersible pumps or rod-driven mechanical pumps) in the portion of thewellbore, and/or passing production equipment through the portion of thewellbore.

SUMMARY

Certain embodiments described herein provide a method for providinginformation regarding the tortuosity of a wellbore path. The methodcomprises receiving data from a plurality of survey stations of awellbore survey. The method further comprises defining a plurality ofreference lines for the wellbore path. The method further comprisesdetermining a plurality of displacements of the wellbore path from theplurality of reference lines.

Certain embodiments described herein provide a computer system forproviding information regarding the tortuosity of a wellbore path. Thecomputer system comprises a memory and a processor. The processor isconfigured to receive data from a plurality of survey stations of awellbore survey. The processor is further configured to define aplurality of reference lines for the wellbore path. The processor isfurther configured to determine a plurality of displacements of thewellbore path from the plurality of reference lines.

Certain embodiments described herein provide a tangiblecomputer-readable medium having instructions stored thereon whichinstruct a computer system to provide information regarding thetortuosity of a wellbore path by at least: receiving data from aplurality of survey stations of a wellbore survey, defining a pluralityof reference lines for the wellbore path, and determining a plurality ofdisplacements of the wellbore path from the plurality of referencelines.

BRIEF DESCRIPTION OF THE DRAWINGS

Various configurations are depicted in the accompanying drawings forillustrative purposes, and should in no way be interpreted as limitingthe scope of the systems or methods described herein. In addition,various features of different disclosed configurations can be combinedwith one another to form additional configurations, which are part ofthis disclosure. Any feature or structure can be removed, altered, oromitted. Throughout the drawings, reference numbers may be reused toindicate correspondence between reference elements.

FIG. 1 schematically illustrates a portion of an example wellbore pathin accordance with certain embodiments described herein.

FIG. 2A is a flow diagram of an example method for providing informationregarding the tortuosity of the wellbore path in accordance with certainembodiments described herein.

FIGS. 2B-2D schematically illustrate the example technique of FIG. 2A.

FIG. 3A is a flow diagram of an example method for providing informationregarding the tortuosity of the wellbore path in accordance with certainembodiments described herein.

FIG. 3B schematically illustrates the example technique of FIG. 3A.

FIGS. 4A-4E schematically illustrate an example procedure fordetermining potential contact points of an elongate structure within thewellbore with an inner surface of the wellbore in accordance withcertain embodiments described herein.

FIG. 5 is an example plot of the normalized displacement as a functionof measured depth for an example rod in an example wellbore inaccordance with certain embodiments described herein.

FIG. 6 shows two plots of the maximum outer diameter of a model devicehaving a length of 100 feet as a function of the measured depth (MD) fora straight non-bendable model device and a straight bendable modeldevice.

FIG. 7A is a flow diagram of an example method for providing informationregarding the tortuosity of the wellbore path in accordance with certainembodiments described herein.

FIG. 7B schematically illustrates an example configuration compatiblewith the example method of FIG. 7A.

FIGS. 8A-8C schematically illustrate example displays in accordance withcertain embodiments described herein.

FIG. 9 schematically illustrates an example display in accordance withcertain embodiments described herein.

FIG. 10 schematically illustrates another example display in accordancewith certain embodiments described herein.

FIGS. 11A and 11B show example three-dimensional renderings of thetransverse displacement measured along a portion of a wellbore inaccordance with certain embodiments described herein.

FIGS. 12A and 12B show example highside, lateral, and total transversedisplacements as a function of measured depth of a portion of a wellborein accordance with certain embodiments described herein.

FIGS. 13A and 13B show an example tortuosity of the wellbore as afunction of measured depth in accordance with certain embodimentsdescribed herein.

FIGS. 14A and 14B show example plots of the maximum outer diameter of amodel device 90 feet long that can be placed at a specific measureddepth along the wellbore in accordance with certain embodimentsdescribed herein.

DETAILED DESCRIPTION

Although certain configurations and examples are disclosed herein, thesubject matter extends beyond the examples in the specifically disclosedconfigurations to other alternative configurations and/or uses, and tomodifications and equivalents thereof. Thus, the scope of the claimsappended hereto is not limited by any of the particular configurationsdescribed below. For example, in any method or process disclosed herein,the acts or operations of the method or process may be performed in anysuitable sequence and are not necessarily limited to any particulardisclosed sequence. Various operations may be described as multiplediscrete operations in turn, in a manner that may be helpful inunderstanding certain configurations; however, the order of descriptionshould not be construed to imply that these operations areorder-dependent. Additionally, the structures, systems, and/or devicesdescribed herein may be embodied as integrated components or as separatecomponents. For purposes of comparing various configurations, certainaspects and advantages of these configurations are described. Notnecessarily all such aspects or advantages are achieved by anyparticular configuration. Thus, for example, various configurations maybe carried out in a manner that achieves or optimizes one advantage orgroup of advantages as taught herein without necessarily achieving otheraspects or advantages as may also be taught or suggested herein.

Information regarding the tortuosity of a newly-drilled wellbore can behelpful in avoiding installing production equipment in portions of thewellbore having high tortuosity. In addition, information regarding thetortuosity may be used to analyze the performance of different drillingmethods (e.g., using rotary steerable tools or bent subs) in differentformations.

It can be advantageous to drill wellbores with low tortuosity (e.g.,wellbores with smooth wellbore trajectories; wellbores with minimalshort-scale variation in the wellbore path) that are consistent with thepredetermined wellbore plan. It can also be advantageous to placeproduction equipment in portions of the wellbore having low tortuosity.Since a rigid item of equipment may not be able to pass through and/orreside in a wellbore section having too great a curvature, informationregarding the tortuosity of the wellbore section can be advantageouslyused (e.g., along with the diameter of the wellbore section) todetermine equipment dimensions (e.g., maximum diameter of a rigid pipeor rod of length L; maximum length of a rigid pipe or rod of diameter D)that may be expected to pass through and/or reside in the wellboresection.

Current systems and methods seeking to provide information regarding thetortuosity of the wellbore path utilize the measured dogleg of thewellbore (e.g., bending of the survey tool when the survey tool is atvarious positions, such as survey stations, along the wellbore path, orchanges in wellbore attitude analyzed from directional survey data).However, information from dogleg curves is, in general difficult to use,for several reasons: (a) if the dogleg is calculated from survey dataobtained at long intervals of measured depth (“MD”), the results canlack sufficient detail; (b) if the dogleg is calculated from survey dataobtained at short MD intervals, the results can in general be noisy; (c)it can be difficult to upgrade from dogleg values over short intervalsto meaningful dogleg values over longer intervals, by for exampleaveraging techniques.

Certain embodiments described herein advantageously provide systems andmethods that provide quantification of the tortuosity of the wellborepath that are not as affected by noise and are easier to use. Certainembodiments described herein advantageously provide systems and methodsfor evaluating the tortuosity of portions of the wellbore using wellboresurvey data. Examples of wellbore survey data in accordance with certainembodiments described herein include, but are not limited to: continuousgyroscopic survey data; gyroscopic survey data with a relatively smalldepth interval between successive surveys, for example, one foot; othersurvey data with sufficiently high spatial resolution along the wellbore(e.g., with sufficiently frequent or short depth intervals), forexample, from inclinometers, accelerometers, measurement-while-drilling(MWD) magnetic instruments, inertial instruments. Certain embodimentsdescribed herein provide a system and method of analyzing wellboresurvey data and generating information regarding the wellbore tortuositythat can be displayed in an effective and useful manner. The tortuositycan be presented in a manner that allows decisions to be made aboutwhere to install equipment in the wellbore after the wellbore has beencreated. In certain embodiments, a method that is implemented on acomputer can be used to analyze and present wellbore tortuosityinformation to a user to make vital decisions about the development of awell.

For example, the tortuosity information can be helpful in determiningwhere to place one or more pumps in the wellbore. The placement of apump in a wellbore section having a relatively high tortuosity canreduce the lifetime of the pump dramatically. If installed in ahigher-tortuosity section of the wellbore, the pump may be subject to abending moment due to the shape of the wellbore restricting the abilityof the pump rotor to turn freely (e.g., as a result of excess pressureon the bearings or sliding contact between the rotor and the outercasing of the pump), causing the pump to wear out sooner than had thepump been installed in a lower-tortuosity section of the wellbore.

FIG. 1 schematically illustrates a portion of an example wellbore pathin accordance with certain embodiments described herein. The examplewellbore path of FIG. 1 has a lower tortuosity on the left side of theillustrated portion of the wellbore path and a higher tortuosity on theright side of the illustrated portion of the wellbore path. The wellborepath typically is a three-dimensional trajectory, which FIG. 1illustrates in two dimensions. The solid circles along the wellbore pathrepresent survey stations at which survey data of the wellboretrajectory have been measured. At each of the survey stations, thethree-dimensional coordinates of the wellbore path can be measured andexpressed, for example, in terms of the parameters of measured depth(MD), inclination (Inc), and azimuth (Az), or in terms of the spatialposition parameters north (N), east (E), and vertical (V). In certainembodiments, the spacings between adjacent survey stations along thewellbore are on the order of one foot (e.g., spacings in a range of onefoot to five feet; spacings of one foot or less). In certainembodiments, survey data measured in (MD, Inc, Az) can be converted into(N, E, V) to enable calculation of distances in NEV space, while incertain other embodiments, conversion of survey data from (N, E, V) into(MD, Inc, Az) may be performed. In certain embodiments, the spacings aresubstantially equal to one another (e.g., the survey stations aresubstantially equidistant from one another along a parameter such asMD), while in certain other embodiments, the spacings vary from oneanother (e.g., the survey stations are not substantially equidistantfrom one another along a parameter such as MD).

As schematically illustrated in FIG. 1, an analysis window may be usedin the analysis of the wellbore survey data, and the tortuosity of theportion of the wellbore path within the analysis window may begenerated. In certain embodiments, the analysis window includes the datafrom survey stations within a predetermined MD length (e.g., a fixed MDlength). In certain other embodiments, the analysis window includes thedata from survey stations within a predetermined number of surveystations along the wellbore path. The analysis window can besequentially set (e.g., moved or slid) along the wellbore path such thatthe tortuosity of subsequent portions of the wellbore path is calculatedsequentially to provide a measure of the tortuosity of the wellborepath. For example, the analysis window can be moved by one surveystation between successive calculations, or the analysis window can bemoved by two or more survey stations between successive calculations. Bysetting the analysis window at sequential positions along the wellborepath, the tortuosity of the wellbore path at these positions can becompared to evaluate which portions of the wellbore path have highertortuosities than others.

In the discussion below, multiple techniques are described for providinginformation regarding the tortuosity of the wellbore path in accordancewith certain embodiments described herein. In certain embodiments, thesetechniques may be used separately from one another, while in certainother embodiments, two or more of these techniques may be used inconjunction with one another. For example, the data may be pre-processedusing one or more of the techniques described below, and then furtherprocessed by one or more other techniques of the techniques describedbelow. Such pre-processing may advantageously facilitate the separationof tortuosity from other effects, such as large-scale wellborecurvature. In certain embodiments, two or more of these techniques maybe used in conjunction with one another in one sequence or order, whilein certain other embodiments, the two or more techniques may be used inconjunction with one another in another sequence or order. Thetechniques can also be used iteratively, e.g., repeated application ofone or more techniques in any conjunction or sequence, for gradualrefinement of the results.

Spectral Analysis Technique

FIG. 2A is a flow diagram of an example method 100 for providinginformation regarding the tortuosity of the wellbore path in accordancewith certain embodiments described herein, and FIGS. 2B-2D schematicallyillustrate the example technique of FIG. 2A. In certain embodiments, themethod 100 provides a spectral analysis technique which allowsinformation to be gathered about the relative distances over whichsignificant variations in well orientation occur.

The method 100 comprises receiving data from a plurality of surveystations of a wellbore survey in an operational block 110. The dataincludes information regarding at least one first parameter of thewellbore path as a function of at least one second parameter of thewellbore path. For example, the data can include information regardingthe inclination (Inc) of the wellbore path as a function of the measureddepth (MD) of the wellbore path, a schematic example of which is plottedin FIG. 2B. For another example, the data can include informationregarding the azimuth (Az) of the wellbore path as a function of themeasured depth (MD) of the wellbore path, a schematic example of whichis plotted in FIG. 2C. The data can be generated during a wellboresurvey with high spatial resolution (e.g., a survey with a short spacingbetween sequential survey stations, for example, less than 30 meters,less than 10 meters, less than 1 meter, less than 0.5 meter, less than0.3 meter, less than 0.1 meter). Such high spatial resolution data canbe used to analyze small-scale wellbore curvature (e.g., having ameasured depth in a range between 1 meter to 100 meters). In certainembodiments, receiving the data comprises generating the data by runninga wellbore survey tool within the wellbore.

The method 100 further comprises performing one or more spectralanalyses within a plurality of portions of the data in an operationalblock 120. For example, as schematically illustrated in FIG. 2C, ananalysis window can denote a portion of the data (e.g., a portion of thewellbore corresponding to the portion of the data is defined by theanalysis window) and the analysis window can be moved (e.g., slid) todenote different portions of the data (denoted in FIG. 2C by thehorizontal arrows). The portions of the data can be sequential to oneanother along the second parameter, and two or more neighboring portionscan overlap one another. For example, the analysis window can be movedbetween successive positions by a predetermined amount (e.g., one surveystation) that is smaller than a width of the analysis window (e.g., 10survey stations). For each portion of the data (e.g., for each positionof the analysis window), a spectral analysis of the portion of the datawithin the analysis window can be performed. For example, a Fouriertransform of the data within the analysis window can be calculated togenerate a spatial frequency relative to the first parameter as afunction of the second parameter. Any spectral transforms that aresuited for analyzing spatial frequencies may be used in accordance withcertain embodiments described herein. For each position of the analysiswindow (e.g., for each value of MD), a range of spectral frequenciesrelative to the Az curve within the analysis window can be generated(e.g., and stored and/or plotted). For example, a range of spectralfrequencies and the relative magnitudes of the spectral frequencieswithin the range can be plotted as a function of the second parameter(e.g., MD) of the wellbore path, as schematically shown by FIG. 2D. Thespectral shape and contents will vary as a function of the secondparameter as the analysis window moves along the data, and the resultantinformation (e.g., presented numerically or as a two-dimensional plot asschematically shown in FIG. 2D), can be used to identify regions ofinterest in the data along the second parameter.

Portions of the data with very low spatial frequencies (e.g., in thecenter of FIG. 2D) can be indicative of low or very low tortuosity ofthe corresponding portions of the wellbore path (e.g., portions in whichthe wellbore path generally follows a smooth curve, such as thepredetermined plan for the wellbore path). Other portions of the datawith relatively low spatial frequencies (e.g., on the left side of FIG.2D) can be indicative of low tortuosity of the corresponding portions ofthe wellbore path (e.g., portions in which the wellbore path generallyfollows a more tortuous curve of the predetermined plan for the wellborepath). Still other portions of the data with relatively high spatialfrequencies (e.g., on the right side of FIG. 2D) can be indicative ofhigh tortuosity of the corresponding portions of the wellbore path(e.g., portions in which the wellbore path is too tortuous for placementof equipment in the wellbore).

In certain embodiments, the resultant spatial frequency information canbe used to identify regions of the survey data in which further analysisis to be performed or parameters to be used in further analysis (e.g.,pre-processing before using one or more of the other techniquesdescribed herein). For example, a threshold level can be predetermined(e.g., the horizontal dotted line of FIG. 2D) to distinguish betweenspatial frequency distributions of low tortuosity (e.g., tortuosity ofless concern and not warranting further analysis) and those of hightortuosity (e.g., tortuosity of more concern and warranting furtheranalysis). In certain embodiments, the resultant spatial frequencyinformation can be used to identify regions of the wellbore in whichequipment (e.g., one or more pumps) are to be placed.

Displacement Technique

FIG. 3A is a flow diagram of an example method 200 for providinginformation regarding the tortuosity of the wellbore path in accordancewith certain embodiments described herein, and FIG. 3B schematicallyillustrates the example technique of FIG. 3A. In certain embodiments,the method 200 provides an analysis based on the variation ininclination and azimuth at one or more positions within the portion ofthe wellbore. In certain other embodiments, the method 200 provides ananalysis based on the variation in north, east, and vertical coordinatesat one or more positions within the portion of the wellbore. In certainembodiments, the tortuosity of the wellbore path is determined byexamining an analysis window (e.g., having a fixed length) as theanalysis window is moved (e.g., slid) along the portion of the wellborepath. The length of the analysis window can be varied to determine thetortuosity over different lengths of the wellbore path. For example, thelength of the analysis window can be selected to be equal to the lengthof a physical device to be inserted into the wellbore, or the length ofthe analysis window can be selected based on the spatial frequencyestimates (e.g., equal to a threshold line value between high frequencyand low frequency values from the spatial frequency plot of the spectralanalysis technique described herein).

The method 200 comprises receiving data from a plurality of surveystations of a wellbore survey in an operational block 210. The dataincludes information regarding a position of the wellbore path at eachsurvey station of the plurality of survey stations. For example, thedata can include information regarding the inclination (Inc), theazimuth (Az), and the measured depth (MD) of the wellbore path at eachsurvey station of the plurality of survey stations (e.g., the pluralityof survey stations that are to be analyzed). For another example, thedata can include information regarding the north, east, and verticalcoordinates of the wellbore path at each survey station of the pluralityof survey stations (e.g., the plurality of survey stations that are tobe analyzed). The data can be generated during a wellbore survey withhigh spatial resolution (e.g., a survey with a short spacing betweensequential survey stations, for example, less than 30 meters, less than10 meters, less than 1 meter, less than 0.5 meter, less than 0.3 meter,less than 0.1 meter). Such high spatial resolution data can be used toanalyze small-scale wellbore curvature (e.g., having a measured depth ina range between 1 meter to 100 meters). In certain embodiments,receiving the data comprises generating the data by running a wellboresurvey tool within the wellbore.

The method 200 further comprises defining a plurality of reference linesfor the wellbore path within a corresponding plurality of analysiswindows in an operational block 220. For example, as schematicallyillustrated in FIG. 3B, an analysis window can be defined to denote acorresponding portion of the data and the analysis window can be moved(e.g., slid) to denote different portions of the data. The portions ofthe data can be sequential to one another, and two or more neighboringportions can overlap one another. For example, the analysis window canbe moved between successive positions by a predetermined amount (e.g.,one survey station) that is smaller than the width of the analysiswindow (e.g., 10 survey stations).

For each portion of the data (e.g., for each position of the analysiswindow), a reference line in three-dimensional (“3D”) space can bedefined within the analysis window based on two or more survey stationswithin the analysis window. FIG. 3B schematically illustrates areference line (“ref. line 1”) for “analysis window 1” and a referenceline (“ref line 2”) for “analysis window 2”. Examples of reference linesthat are compatible with certain embodiments described herein include,but are not limited to:

-   -   a straight reference line defined by the positions of the first        and last survey stations of the analysis window;    -   a straight reference line defined by the weighted best fit of        the positions of the survey stations of the analysis window to a        straight line (e.g., the weighted best first-order fit);    -   a curved reference line defined by the weighted best fit of the        positions of the survey stations of the analysis window to a        curved line (e.g., the weighted best higher-order fit);    -   a curved reference line resulting from spatial low-pass        filtering of one or more of the parameters Inc, Az, N, E, V, as        a function of MD.    -   an iteratively derived line which is derived by calculating        deviations of the wellbore path from an initial reference line        (e.g., straight or curved), updating station positions with        these deviations (e.g., either fully or partially) to bring them        closer to the reference line, where repetition of this procedure        will gradually smooth the curve with the final smoothed curve        serving as the reference line.        In certain embodiments, the reference line resulting from the        processing described above can be used to modify the original        wellbore path (e.g., by subtraction) to retain only the higher        spatial frequency (e.g., small-scale) variations.

The method 200 further comprises determining a plurality ofdisplacements in 3D space of the wellbore path from the plurality ofreference lines within the plurality of analysis windows in anoperational block 230. For each analysis window, a displacement of thewellbore path can be determined at one or more predetermined positionswithin the analysis window (e.g., at a survey station in the center ofthe analysis window, as shown schematically in FIG. 3B). Thedisplacement (e.g., labeled “P1” for “Analysis window 1” and “P2” for“Analysis window 2”) can comprise a direction and a magnitude of thedisplacement vector (e.g., a vector that is perpendicular to thereference line and that points to the position of the survey station atwhich the displacement is determined). In certain embodiments, thedisplacements can be calculated directly from wellbore data (e.g., Inc,Az, N, E, V) that have been high-pass filtered with respect to spatialfrequency along MD. The high-pass filtering can remove thelow-spatial-frequency components that constitute the reference line orreference curve discussed above. In certain other embodiments, thedisplacement vector can be calculated from a vector that projects thesurvey station onto the reference line, or from a vector that connectsthe survey station and the midpoint of the reference line, or from avector that connects the survey station and the middle position of theset of survey stations used to find the reference line.

Portions of the data in which the displacement has relatively smallmagnitude or varies slowly along the wellbore (e.g., slowly withmeasured depth, as in the region of the wellbore near “analysis window1” of FIG. 3B) can be indicative of lower tortuosity of thecorresponding portions of the wellbore path (e.g., portions in which thewellbore path generally follows the predetermined plan for the wellborepath). Still other portions of the data in which the displacement hasgreater magnitude or varies more rapidly along the wellbore (e.g., morerapidly with measured depth, as in the regions of the wellbore near“analysis window 2” of FIG. 3B) can be indicative of high tortuosity ofthe corresponding portions of the wellbore path (e.g., portions in whichthe wellbore path is too tortuous for placement of equipment in thewellbore).

In certain embodiments, the displacements found by this technique can besubtracted (e.g., fully or partially) from the wellbore path to generatea smoothed wellbore curve (e.g., in a single step or in an iterativeprocedure), or the displacements can be used to establish a smoothedwellbore curve via curve-fitting. In certain embodiments, subtractingthe smoothed wellbore curve from the wellbore path can illustrate onlythe high-frequency (e.g., small scale) variations of the wellbore path.One or more of the techniques described herein can then be applied tothe resulting data having these high-frequency variations.

In certain embodiments, the displacements can be calculated directly onat least one of the inclination data and the azimuth data, and can beused to generate a smoothed wellbore curve. In certain embodiments, thedata can advantageously be converted to NEV space prior to the smoothingprocedure, since in NEV space, the displacements are true displacements,not mere angular dimensions.

Contact Points

In certain embodiments, the information regarding the tortuosity of thewellbore path can be expressed as a series of potential points ofcontact between an elongate structure within the wellbore and an innersurface of the wellbore (e.g., points at which the elongate structurecan potentially contact the inner surface of the wellbore due to thetortuosity of the wellbore path). For example, the elongate structurecan comprise a rod, a portion of a rod, a rod guide, or a portion of arod guide used as part of a wellbore pumping system.

The rod or rod guide can be configured to be used as part of a wellborepumping system. For example, a beam pumping system can utilize a rodwhich is configured to be mechanically coupled to a downhole pump and toan above-ground drive unit. In a reciprocating rod lift (RRL) pumpingsystem (e.g., an artificial lift configuration), the rod can be referredto as a “sucker rod” and the drive unit can be configured to move thesucker rod axially (e.g., up and down) within the wellbore to actuatethe downhole pump. The sucker rod can comprise a plurality of rodportions that are coupled (e.g., jointed) to one another (e.g., bythreaded ends). A variety of types of sucker rods can be used (e.g.,API, non-API, hollow, fiberglass, fiber-reinforced plastic, highstrength) and the rod portions can have a variety of lengths, diameters,and tensile strengths. In a progressing cavity pumping (PCP) system(sometimes referred to as a progressive cavity pumping system), the rodrotates, rather than moving axially, to apply movement to the downholepump.

Where the rod comes into contact with an inner surface of the wellbore(e.g., an inner wall of a wellbore casing or other tubular structurewithin the wellbore), the rod can be subject to bending moments andwear. In certain such instances, one or more rod guides or rod guideportions can be inserted at appropriate locations within the wellbore toallow the rod to move smoothly within the wellbore and to reduce wear.In addition, the bending moments can be quantified and compared to therod manufacturer's specifications to give forewarning of possibleproblems with the rods. Certain embodiments described herein can be usedto determine locations of potential contact points between the rod andthe inner surface of the wellbore and hence, where to install one ormore rod guides.

FIGS. 4A-4E schematically illustrate an example procedure fordetermining potential contact points of an elongate structure (e.g., arod, a rod guide, or a portion thereof) within the wellbore with aninner surface of the wellbore in accordance with certain embodimentsdescribed herein. The potential contact points can be points at whichthe elongate portion is estimated to contact the inner surface of thewellbore. The example procedure of FIGS. 4A-4E can be considered anexample of the method 200 illustrated in FIG. 3A. For example, using thedata provided from the plurality of survey stations of a wellbore survey(e.g., in the operational block 210 of the method 200), a plurality ofreference lines for the wellbore path within a corresponding pluralityof analysis windows can be defined (e.g., in the operational block 220of the method 200), and a plurality of displacements of the wellborepath from the plurality of reference lines can be determined (e.g., inthe operational block 230 of the method 200).

FIG. 4A schematically illustrates an example of defining a referenceline in accordance with certain embodiments described herein. Thewellbore comprises a center line, referred to in FIG. 4A as a wellpath,which can be defined using the data provided from the plurality ofsurvey stations. A boundary defining a volume within the wellbore inwhich equipment can travel can be defined using the data provided fromthe plurality of survey stations and known physical dimensions (e.g.,inner radius of the wellbore, inner radius of wellbore casings). FIG. 4Aalso shows a series of survey stations S₀, . . . , S_(n) along thewellpath. Only some of the survey stations (e.g., S₀, S₅, S₁₀, S₁₂, S₁₄,S₁₅, S₁₆, S₁₈, S₂₂, S₂₈, S₄₃) are shown explicitly in FIG. 4A forclarity. By applying the reference line and displacement processingmethod described herein, a first reference line can be defined as thelongest line which extends from the survey station S₀ to a subsequentsurvey station, and does not extend past the boundary (e.g., defined bythe inner radius r_(wc) of the wellbore casing surrounding the wellpath)defining the volume within the wellbore in which equipment can travel.For example, the first reference line can be defined as the longest lineextending from the survey station S₀ to a subsequent survey station(e.g., S₁, S₂, S₃, . . . , S_(n)) that does not extend past the innerwall of the wellbore casing. More generally, a reference linecorresponding to a survey station S_(n) can be defined as the longestline which extends from the survey station S_(n) to a subsequent surveystation, and does not extend past the boundary defining the volumewithin the wellbore in which equipment can travel.

Such a reference line can be found by defining a plurality of candidatereference lines as straight lines between the survey station (e.g., S₀)and a number N of subsequent survey stations (e.g., S_(i) where i=1 . .. N, with N being user-defined). The plurality of N candidate referencelines for the survey station S₀ can be referred to as S₀S₁, S₀S₂, . . ., S₀S_(i), . . . S₀S_(N). For each candidate reference line, thetransverse displacements of the candidate reference line from eachsurvey station between the two survey stations at the two ends of thecandidate reference line can be determined. For example, for thecandidate reference line S₀S₂₂, the transverse displacements of thecandidate reference line S₀S₂₂ can be determined at each survey stationS₁, . . . , S₂₁. Still for each candidate reference line, the maximumtransverse displacement of the candidate reference line from each surveystation can be determined and compared to the boundary defining thevolume within the wellbore in which equipment can travel (e.g., comparedto an inner radius of the wellbore or of the casing or tubing within thewellbore, perhaps corrected for the finite diameter of the rod orinternal tubing). For example, if the maximum transverse displacement ofthe candidate reference line is less than the inner radius, then thecandidate reference line lies wholly inside the volume. If the maximumtransverse displacement of the candidate reference line is greater thanthe inner radius, then the candidate reference line extends outside thevolume. If the maximum transverse displacement of the candidatereference line is equal to the inner radius, then the candidatereference line touches the boundary of the volume. Based on suchcomparisons, the reference line corresponding to the survey station canbe selected.

As shown in FIG. 4A, for the survey station S₀, the line S₀S₁₄ lieswholly within the wellbore casing (e.g., does not touch or extend pastthe inner wall of the wellbore casing), while the line S₀S₁₅ touches anddoes not extend past the wellbore casing (e.g., touches and does notextend past the inner wall of the wellbore casing), and each of thesubsequent lines (e.g., S₀S₁₆, S₀S₁₈, and S₀S₂₂) extends past the innerwall of the wellbore casing. The reference line corresponding to thesurvey station S_(n) can be defined to be the line S_(n)S_(j) for whichit and all “previous” lines (e.g., SS_(n)S_(k) (with k=n+1, . . . , j)do not extend past the boundary defining the volume within the wellborein which equipment can travel, and the “next” line S_(n)S_(j+1) doesextend past the boundary. Using this definition in the example of FIG.4A, the reference line corresponding to the survey station S₀ (e.g., thefirst reference line) is the line S₀S₁₅, since this line and all“previous” lines S₀S_(k) (with k=1, . . . , 15) do not extend past theboundary defining the volume within the wellbore in which equipment cantravel, and the “next” line S₀S₁₆ does extend past the boundary.

In certain other embodiments, the reference lines can be defineddifferently. For example, the reference line can be defined as being thelongest line which extends from the corresponding survey station to asubsequent survey station, and does not touch or extend past theboundary. Using this alternative definition in the example of FIG. 4A,the first reference line would be the line S₀S₁₄ since this line is thelongest line extending from the survey station S₀ to a subsequent surveystation that does not touch or extend past the inner wall of thewellbore casing. For another example, the reference line can be definedas being the shortest line which extends from the corresponding surveystation to a subsequent survey station, and which extends past theboundary. Using this alternative definition in the example of FIG. 4A,the first reference line would be the line S₀S₁₆ since this line is theshortest line extending from the survey station S₀ to a subsequentsurvey station that extends past the inner wall of the wellbore casing.For another example, the reference line can be defined as being thelongest line which extends from the corresponding survey station to asubsequent survey station, and does not extend past the boundary. Thus,the reference line corresponding to the survey station S₀ (e.g., thefirst reference line) can be defined to be the line S₀ 5 ₁₅ since it isthe longest line that extends from the survey station S₀ to a subsequentsurvey station and does not extend past the boundary defining the volumewithin the wellbore in which equipment can travel. Using thisdefinition, it does not matter if there are any shorter lines whichextend past the boundary. For another example, the reference line can bedefined as being the “next” line after the longest line which extendsfrom the corresponding survey station to a subsequent survey station,and does not extend past the boundary.

A maximum displacement d₁ of the wellbore path from the first referenceline can be determined and the location C₁ of this maximum displacementd₁ can be determined and marked as an estimated location of a firstcontact point. For example, the maximum displacement d₁ of the wellborepath from the first reference line can be equal to the maximum distancebetween the wellbore path and the first reference line in a directionperpendicular to the first reference line, and the location along thewellbore path from which this maximum displacement d₁ is measured can bemarked as the estimated location C₁ of the first contact point. Theestimated location C₁ is at the location of a subsequent survey stationto the survey station S₀ corresponding to the first references line, andthis maximum displacement d₁ of the wellbore path is the maximumtransverse displacement that was determined for selecting the firstreference line, as described above. Using the example first referenceline S₀S₁₅ shown in FIG. 4A, the maximum displacement d₁ is shown by thedouble-headed arrow and its location along the wellbore path is at thelocation labeled C₁. In certain embodiments, the location C₁ of thefirst contact point is taken to be the location of the closest surveystation at which the maximum displacement d₁ occurs. For example, usingthe example first reference line S₀S₁₅ of FIG. 4A, the location C₁ ofthe first contact point can be taken to be the location of surveystation S₈ (not shown).

Note that using each of the example definitions of the first referenceline described above, the maximum displacements d₁ between the firstreference line and the wellbore path are approximately equal to oneanother (e.g., approximately equal to the inner radius of the wellborecasing). Also, using each of the example definitions of the firstreference line described above, the locations C₁ of the first contactpoint are approximately equal to one another.

To determine an estimated location of a second contact point C₂, asecond reference line can be defined as the longest line which extendsfrom the estimated location of the first contact point C₁ to asubsequent survey station (e.g., S₉, S₁₀, . . . , S_(n)), and thattouches and does not extend past the boundary defining the volume withinthe wellbore in which equipment can travel. For example, using theexample of FIG. 4A, the second reference line can be the line C₁S₂₈since this line is the longest line which extends from the first contactpoint C₁ to a subsequent survey station (e.g., S₂₈), and that touchesand does not extend past the boundary. While not shown in FIG. 4A, theline C₁S₂₇ lies wholly within the wellbore casing (e.g., does not touchor extend past the inner wall of the wellbore casing), and the lineC₁S₂₉ extends past the inner wall of the wellbore casing. Thus, thesecond reference line is the line C₁S₂₈ since it extends from theestimated location of the first contact point C₁ to a subsequent surveystation (S₂₈) and touches and does not extend past the boundary definingthe volume within the wellbore in which equipment can travel.

As described above with regard to the first reference line, in certainother embodiments, the second reference line can be defined differently.For example, the second reference line can be defined as being thelongest line which extends from the first contact point C₁ to asubsequent survey station, and does not touch or extend past theboundary (e.g., the line C₁S₂₇). For another example, the secondreference line can be defined as being the shortest line which extendsfrom the first contact point C₁ to a subsequent survey station, andwhich extends past the boundary (e.g., the line C₁S₂₉).

In a manner similar to that described above for determining the maximumdisplacement d₁, a maximum displacement d₂ of the wellbore path from thesecond reference line C₁S₂₈ (e.g., equal to the maximum distance betweenthe wellbore path and the second reference line C₁S₂₈ in a directionperpendicular to the second reference line C₁S₂₈) can be determined andthe location C₂ of this maximum displacement d₂ along the wellbore pathcan be determined and marked as an estimated location of a secondcontact point.

As described above with regard to the first reference line, in certainembodiments, the location C₂ of the second contact point is taken to bethe location of the closest survey station at which the maximumdisplacement d₂ occurs. For example, using the example second referenceline C₁S₂₈, the location C₂ of the second contact point can be taken tobe the location of survey station S₂₃ (not shown). In certain otherembodiments, the location C₂ of the second contact point is taken to bethe actual location at which the maximum displacement d₂ occurs (e.g.,at a location between two adjacent survey stations; at an interpolatedlocation between two adjacent survey stations).

This procedure can be repeated for subsequent contact points, bydefining subsequent reference lines similarly to the definitions of thefirst and second reference lines. The maximum displacements of thewellbore path from these subsequent reference lines can be determinedsimilarly to the determinations of the maximum displacements describedabove and the locations of these maximum displacements can be determinedsimilarly to the determinations of the locations described above andmarked as estimated locations of the subsequent contact points. FIG. 4Bschematically illustrates a series of reference lines and estimatedlocations of three contact points C₁, C₂, C₃ of the wellbore shown inFIG. 4A determined in accordance with certain embodiments describedherein.

In the example embodiment described above, the reference lines aredefined without accounting for the radius r_(es) of the elongatestructure. In certain other embodiments, the radius r_(es) of theelongate structure can be taken into account by defining each referenceline. For example, the reference lines can be defined as the longestlines which touch and do not extend past a boundary that surrounds thewellpath and that has an inner radius equal to the inner radius r_(wc)of the wellbore casing minus the radius r_(es) of the elongatestructure. For another example, the reference lines can be defined asbeing the longest lines which do not touch or extend past the boundarythat surrounds the wellpath and that has an inner radius equal to theinner radius r_(wc) of the wellbore casing minus the radius r_(es) ofthe elongate structure. For another example, the reference lines can bedefined as being the shortest lines which extend past the boundary thatsurrounds the wellpath and that has an inner radius equal to the innerradius r_(wc) of the wellbore casing minus the radius r_(es) of theelongate structure.

In certain embodiments, the estimated location of a contact point can beadjusted using an adjustment reference line defined using the othercontact points. For example, FIG. 4C schematically illustrates a seriesof adjustment reference lines, each corresponding to a contact pointC_(n) and defined as extending from the previous contact point C_(n−1)to the subsequent contact point C_(n+1). The estimated location of eachcontact point C_(n) can be moved from its initial estimated location toan adjusted estimated location C equal to the location of maximumdisplacement d′_(n) of the reference line C_(n-1)C_(n+1) from thewellpath. Such an adjustment procedure can result in large adjustmentsof some estimated contact point locations (e.g., C′₁) and smalleradjustments of other estimated contact point locations (e.g., C′₂). Incertain embodiments, the initial estimated locations of a series ofcontact points C_(n) can be determined, and then a corresponding seriesof adjusted estimated locations of the series of contact points C′_(n)can be determined. For example, the initial estimated locations of atrio of adjacent contact points C_(n−1), C_(n), C_(n+1) can bedetermined, and the adjusted estimated locations of the contact pointC′_(n) can be determined before proceeding to determine the subsequentadjusted estimated location of the contact point C′_(n+1) using thesubsequent trio of adjacent contact points C_(n), C_(n+1), C_(n+2). Incertain embodiments, an adjusted estimated location of a contact pointC′_(n) can be used to determine a subsequent adjusted estimated locationof a contact point C′_(n+1). For example, as shown in FIG. 4C, theinitial estimated locations of the contact points C₀, C₁, C₂, C₃ can bedetermined as described above, and the initial estimated locations ofthe contact points C₀ and C₂ can be used to determine the adjustedestimated locations of the contact point C′₁, and the adjusted estimatedlocation of the contact point C′₁ and the initial estimated location ofthe contact point C₃ can be used to determine the adjusted estimatedlocation of the contact point C′₂.

Determining the initial estimated locations and the adjusted estimatedlocations can be performed in other orders as well in accordance withcertain embodiments described herein. In addition, determining theadjusted estimated locations can be performed by iteration. For example,the iteration can include determining the initial estimated locations ofsome or all of the contact points C_(n), determining first adjustedestimated locations of some or all of the contact points C′_(n), anddetermining second adjusted estimated locations of some or all of thecontact points C″_(n) (e.g., using the first adjusted estimatedlocations of the contact points C′_(n)), etc. Such iterations can beperformed to refine the adjusted estimated locations until apredetermined number of iterations is performed or until the differencebetween sequential iterations is less than a predetermined limit.

In certain embodiments, it is of interest to quantify the amount ofcurvature or bending of the elongate structure at a contact point withinthe wellbore. FIG. 4D schematically illustrates an examplequantification of the degree of bend at a contact point in accordancewith certain embodiments described herein. The length L_(n−1,n+1) of thestraight line C_(n−1)C_(n+1) extending between contact point C_(n−1) andcontact point C_(n+1) can be calculated and the maximum displacementd_(n) of the contact point C_(n) can also be calculated. A normalizeddisplacement (d_(n)/L_(n−1,n+1)) equal to the maximum displacement d_(n)divided by the length L_(n−1,n+1) of the straight line can be calculatedand used as a quantification of the degree of bend at the contact pointC_(n). If the adjustment procedure described above is used, thenormalized displacement (d′_(n)/L′_(n−1,n+1)) can be calculated to beequal to the maximum displacement d′_(n) of the adjusted contact pointC′_(n) from the line C′_(n−1)C′_(n+1) divided by the length L′_(n−1,n+1)of the line C′_(n−1)C_(n+1).

FIG. 4E schematically illustrates a projected trajectory of an elongatestructure (e.g., a rod, a rod guide, or a portion thereof) in accordancewith certain embodiments described herein. In certain embodiments, theprojected trajectory can be used to show locations at which a rod guideis to be placed within the wellbore so as to provide protection of a rodfrom excessive wear.

FIG. 5 is an example plot of the normalized displacement (dimensionless)as a function of measured depth for an example rod in an examplewellbore in accordance with certain embodiments described herein. Thenormalized displacement is calculated as described above with regard toFIG. 4D. The plot of FIG. 5 shows about 70-80 contact points along thewellbore, and the normalized displacement at each contact point can beproportional to the amount of bending that the rod will undergo in aregion near the contact point.

In certain embodiments, a threshold level of the normalized displacementcan be predetermined (e.g., set by an operator while analyzing the dataprovided from the plurality of survey stations). Some or all of thenormalized displacements can be compared to the threshold level, andcontact points having normalized displacements that are greater than orequal to the threshold level can be considered to be potential locationsalong the wellpath for rod guides to be placed. Contact points havingnormalized displacements that are less than the threshold level can beconsidered to be locations along the wellpath that do not need rodguides.

Effective Inner Diameter Technique

Various methods for providing information regarding the tortuosity ofthe wellbore path can utilize example tortuosity parameters inaccordance with certain embodiments described herein. For example, anexample tortuosity parameter can be based on an effective inner diameter(D_(eff)) for the portion of the wellbore, with D_(eff) defined as amaximum width of an outer periphery of a model device with a specified(e.g., predetermined) length that can be placed at, or passed through,the portion of the wellbore. For example, D_(eff) for the portion of thewellbore can be defined as the maximum allowed outer diameter of a modelstraight tubular device with a specified (e.g., predetermined) lengththat can be placed at, or passed through, the portion of the wellbore.The model device can be a hypothetical device with one or moredimensions that are maximized within specified (e.g., predetermined)constraints to characterize the portion of the wellbore in which themodel device is modeled to be placed at or passed through. The modeldevice can be configured to approximate an actual device intended to beplaced at, or passed through, the portion of the wellbore.

The wellbore has an actual inner diameter (D_(actual)) at each surveystation along the wellbore, which can be approximately equal at eachsurvey station or which can vary as a function of survey station. If thetransverse displacements of the wellbore (e.g., displacements in adirection perpendicular to the along-hole direction of the wellborebetween two or more survey stations) are equal to zero, then the D_(eff)for the portion of the wellbore would be largely based on theD_(actual). For example, the D_(eff) between two survey stations of aportion of the wellbore with zero transverse displacements would beapproximately equal to the minimum D_(actual) between the two surveystations. However, a non-zero transverse displacement of the wellborebetween two or more survey stations can reduce the area through whichcasings, equipment, etc. can be inserted, thereby making the D_(eff) forthe portion of the wellbore less than the minimum D_(actual) of theportion of the wellbore.

In the example mentioned above, D_(eff) for the portion of the wellborecan be defined as the maximum allowed outer diameter of a model straighttubular device with a specified (e.g., predetermined) length that can beplaced at, or passed through, the portion of the wellbore. Thus, in thisexample, D_(eff) would be dependent upon the length (L) of the modeldevice to be placed at, or passed through, the portion of the wellbore.For example, if L increases, D_(eff) either remains the same (e.g., ifthe addition to L does not include wellbore sections with additionalrestrictions), or D_(eff) reduces (e.g., if the addition to L doesinclude wellbore sections with additional restrictions). The general andexpected trend is therefore that D_(eff) decreases as L increases, andvice versa. For some simple model geometries, the relation betweenD_(eff) and L can be derived, with the actual formula depending on thespecified model geometry. For actual field data, the relation would bean unknown function.

In certain embodiments, the determination of D_(eff) for a portion ofthe wellbore can be based on the maximum transverse displacement foundover the relevant portion of the wellbore. For example, to determine themaximum transverse displacement, the transverse displacements of theindividual survey stations along the relevant portion of the wellborecan be considered, and the largest of these transverse displacements canbe defined to be the maximum transverse displacement. For anotherexample, to determine the maximum transverse displacement, variouscombinations of the transverse displacements of any two or more surveystations can be considered. For example, the largest difference betweenthe transverse displacements of any two survey stations along theportion of the wellbore can be defined to be the maximum transversedisplacement. The maximum transverse displacement can be defined inother ways in accordance with certain embodiments described hereinbesides these examples.

In certain embodiments, whether the model device can be placed at, orpassed through, the portion of the wellbore is determined based on theamount of transversal (e.g., bending) forces (F) that the model devicewould experience while the model device is within the portion of thewellbore, the amount of transversal (e.g., bending) moment (M) that themodel device would experience while the model device is within theportion of the wellbore, or both. For example, D_(eff) for the portionof the wellbore can be defined as the maximum outer diameter of themodel device such that the model device would experience an amount oftransversal (e.g., bending) forces that are less than or equal to aspecified (e.g., predetermined) limit (F₀) which can be greater than orequal to zero (e.g., F<=F₀ with F₀>=0). For another example, D_(eff) forthe portion of the wellbore can be defined as the maximum outer diameterof the model device such that the model device would experience anamount of transversal (e.g., bending) moments that are less than orequal to a specified (e.g., predetermined) limit (M₀) which can begreater than or equal to zero (e.g., M<=M₀ with M₀>=0). The values of F₀and M₀ can depend on various considerations, including but not limitedto, the type of the device, manufacturer's specifications for thedevice, operational conditions for the device, previous experience withequipment similar to the device, and operator's requirements with regardto functionality and/or lifetime.

Conceptually, there are three general situations (e.g., types ofpositions) in which a device can be placed within a portion of thewellbore. In a first situation, the device is not subject to bendingforces or moments due to the constrained dimensions of the portion ofthe wellbore. Such situations are the most desirable from an operationalviewpoint in which to place the device, not only because the deviceretains its shape (e.g., straight) in such situations, but also becausethe device would be relatively stress-free and would not experience anyoperational degradation due to bending forces or moments.

In a second situation, the device is subject to non-zero bending forcesor moments that are below the level of bending forces or moments thatwould create significant stresses within the device that would causeappreciable operational degradation of the device. In certain suchsituations, the device retains its shape (e.g., straight) despiteexperiencing non-zero bending forces or moments, and while the devicedoes experience some amount of stress, little or no operationaldegradation results. In certain other such situations, for devices thathave been designed to withstand a specified (e.g., predetermined) amountof shape alteration (e.g., bending), the shape of the device can bealtered (e.g., bent) but the stresses remain sufficiently low thatlittle or no operational degradation results. The levels of bendingforces or moments that would create stresses that would causeoperational degradation can be used to define the correspondingspecified (e.g., predetermined) limits F₀ and M₀ described above.

In a third situation, the device is subject to bending forces or momentsthat are greater than or equal to the levels that would create stressesor would alter the shape of the device so as to cause at least someoperational degradation. From an operational viewpoint, these situationsare the least desirable, because the device would be experiencingoperational degradation due to the significant bending forces ormoments. However, while it can generally be desirable to avoid placingthe device in such situations, complete avoidance may not always bepractical in certain circumstances.

In certain embodiments, manufacturer's recommendations for the operationof the device can be used to determine where the device is to be placed(e.g., to place the device either in the first or second situations, butnot in the third situation). For example, a manufacturer'srecommendation that the device be placed in a portion of the wellborethat has less than two degrees of dogleg severity can be used todifferentiate between portions of the wellbore at which the device wouldbe in the undesirable third situation (e.g., where the dogleg severityis greater than or equal to two degrees) or in either of the desirablefirst or second situations (e.g., where the dogleg severity is less thantwo degrees).

In certain embodiments, D_(eff) is defined based on geometricconsiderations, including but not limited to: device length; deviceshape (e.g., variations of the cross-sectional dimensions along thedevice); and the maximum amount of bending allowed for the device. Themaximum amount of bending allowed for the device can depend on theoperational performance expected (e.g., desired) from the device, sincehigher amounts of bending can generally correspond to decreasedoperational performance. Examples of such operational performancefactors include, but are not limited to: general aging and changes overtime (e.g., caused by changing temperature, pressure, or productionconditions), equipment wear, friction, power requirements, deviceinstallment procedures, operation, functionality, performance, orlifetime, or any combination of such factors. For example, if increasedwear, increased power consumption, or reduced lifetime can be toleratedfrom the device, then a higher maximum amount of bending may be allowedfor the device. In addition, these operational performance factors canbe used in combination with the transversal forces (F) or transversalmoments (M) experienced by the model device.

In certain embodiments, rather than being defined as the maximum allowedouter diameter of a model straight tubular device with a specified(e.g., predetermined) length, D_(eff) for the portion of the wellborecan be defined as the maximum allowed outer diameter of a model tubulardevice that can be placed at, or passed through, the portion of thewellbore with a specified (e.g., predetermined) length and configured towithstand a specified (e.g., predetermined) amount of bending (e.g., adegree of curvature). The bending of the model device can be selected toapproximate the amount of bending that an actual device can be expectedto withstand under normal operation and that is likely to not affect thelife of the device.

By allowing the model device to bend, D_(eff) for the portion of thewellbore would be calculated to be larger than it would if the modeldevice were constrained to not bend. For example, the model device canbe allowed to bend by an angle in the range of zero to five degrees per100 feet of length. The amount of bend that is allowed can depend onvarious considerations, including but not limited to, the type of thedevice, manufacturer's specifications for the device, operationalconditions for the device, previous experience with equipment similar tothe device, and operator's requirements with regard to functionalityand/or lifetime. FIG. 6 shows two plots of the maximum outer diameter ofa model device having a length of 100 feet as a function of the measureddepth (MD) of the model device within a wellbore. A first plot of FIG. 6(labeled “Straight Device”) corresponds to a model straight andnon-bendable device and a second plot of FIG. 6 (labeled “CurvedDevice”) corresponds to a model straight device that is configured tobend by at most two degrees across the 100-foot length of the modeldevice. As seen in FIG. 6, the maximum outer diameter (D_(eff))determined using the bendable device is larger at all positions alongthe wellbore than that determined using the non-bendable device. Exceptfor a region near a measured depth of 3000 feet, D_(eff) determinedusing the bendable device approximates the maximum inner diameter of 6inches of the wellbore.

In certain embodiments, rather than using D_(eff) for the portion of thewellbore defined as the maximum allowed outer diameter of a modeltubular device with a specified (e.g., predetermined) length, a maximumdevice length (L_(max)) can be defined as the maximum allowed length ofa model tubular device that can be placed at, or passed through, theportion of the wellbore with a specified (e.g., predetermined) outerdiameter of the device. For example, L_(max) can be defined as themaximum length of the model device such that the model deviceexperiences an amount of transversal (e.g., bending) forces F, momentsM, or both that are less than or equal to corresponding specified (e.g.,predetermined) limits (F₀, M₀). In certain embodiments, both D_(eff) forthe portion of the wellbore and L_(max) of the model device can bedefined and used, such that the model device experiences an amount oftransversal (e.g., bending) forces F, moments M, or both that are lessthan or equal to corresponding specified (e.g., predetermined) limits(F₀, M₀). For example, both D_(eff) for the portion of the wellbore andL_(max) of the model device can be determined, either simultaneously oriteratively (e.g., first adjusting D_(eff), then adjusting L_(max) thenadjusting D_(eff), then adjusting L_(max), etc.), such that thetraversal (e.g., bending) forces F, moments M, or both are less than orequal to corresponding specified (e.g., predetermined) limits (F₀, M₀).

In certain embodiments, the model device can have a non-circularcross-section in a plane perpendicular to a direction along the lengthof the model device, it can have a varying outer diameter along thelength of the model device, or both. In certain such embodiments,D_(eff) can be taken as a characteristic transverse dimension of themodel device (e.g., the maximum transverse dimension of the modeldevice).

In certain embodiments, the wellbore or casing can have a non-circularcross-section in a plane perpendicular to a direction along the lengthof the wellbore or casing, it can have a varying inner diameter alongthe length of the wellbore or casing, or both. In certain suchembodiments, the actual inner diameter can be taken as a characteristictransverse dimension of the wellbore or casing (e.g., the minimumtransverse dimension of the wellbore or casing).

Path Elongation Technique

The preceding section discloses an example method for providinginformation regarding the tortuosity of the wellbore path. FIG. 7A is aflow diagram of an example method 300 for providing informationregarding the tortuosity of the wellbore path in accordance with certainembodiments described herein, and FIG. 7B schematically illustrates anexample configuration compatible with the example method 300 of FIG. 7A.The example method 300 utilizes an example tortuosity parameter (T)which is indicative of the tortuosity of a corresponding portion of thewellbore. For example, the tortuosity parameter T can depend on a ratioof a distance (S) along the wellbore path between two survey stationsand a straight-line distance (L) between the two survey stations (e.g.,T=S/L; T=S/L−1; other functions of S/L) in accordance with certainembodiments described herein. Either or both of the distances S and Lcan alternatively be measured along lines resulting from pre-processing(e.g., smoothing) of the wellbore path between two stations, such that Sis measured along one pre-processed line, and L is measured alonganother pre-processed line, and the pre-processing is defined such thatS>=L. For example, if S is the measured depth between two stations alongthe original wellbore path and L is a measured depth along apre-processed or smoothed path, which can be a straight line or a curvedline, the resulting ratio S/L will provide a measure of short-scaletortuosity along the wellbore path.

Another example tortuosity parameter (T) can be calculated by summingthe magnitudes of displacements (e.g., in a direction generallyperpendicular to the wellbore path) of a reference line defined by twosurvey stations bounding a section of the wellbore (see, e.g., FIG. 3B)and dividing the sum by the straight-line distance (L) between the twosurvey stations (e.g., the length of the reference line). Othertortuosity parameters are also compatible with the various embodimentsdescribed herein to quantify the tortuosity of portions of the wellbore.

The tortuosity parameter will equal a certain value for a perfectlystraight wellbore portion, and will differ from that value for a bendingwellbore portion, by an amount that increases as perturbations of thewellbore path increase. In certain embodiments, the tortuosity of thewellbore path is determined by examining an analysis window (e.g.,having a fixed length) as the analysis window is moved (e.g., slid)along the portion of the wellbore path. The length of the analysiswindow can be varied to determine the tortuosity over different lengthsof the wellbore path. For example, the length of the analysis window canbe selected to be equal to the length of a physical device to beinserted into the wellbore, or the length of the analysis window can beselected based on the spatial frequency estimates (e.g., equal to athreshold line value between high frequency and low frequency valuesfrom the spatial frequency plot of the spectral analysis techniquedescribed herein). The method 300 and the method 200 can be consideredto be complimentary to one another.

The example method 300 comprises receiving data from a plurality ofsurvey stations of a wellbore survey in an operational block 310. Thedata includes information regarding a position of the wellbore path ateach survey station of the plurality of survey stations. For example,the data can include information regarding the inclination (Inc), theazimuth (Az), and the measured depth (MD) of the wellbore path at eachsurvey station of the plurality of survey stations (e.g., the pluralityof survey stations that are to be analyzed). For another example, thedata can include information regarding the north (N), the east (E), andthe vertical (V) coordinates of the wellbore path at each survey stationof the plurality of survey stations (e.g., the plurality of surveystations that are to be analyzed). The data can be generated during awellbore survey with high spatial resolution (e.g., a survey with ashort spacing between sequential survey stations, for example, less than30 meters, less than 10 meters, less than 1 meter, less than 0.5 meter,less than 0.3 meter, less than 0.1 meter). Such high spatial resolutiondata can be used to analyze small-scale wellbore curvature (e.g., havinga measured depth in a range between 1 meter to 100 meters). In certainembodiments, receiving the data comprises generating the data by runninga wellbore survey tool within the wellbore.

The example method 300 further comprises determining a plurality oftortuosity parameter values for the wellbore path within a correspondingplurality of analysis windows in an operational block 320. For example,as schematically illustrated in FIG. 7B, an analysis window can bedefined to denote a portion of the data and the analysis window can bemoved (e.g., slid) to denote different portions of the data. Theportions of the data can be sequential to one another, and two or moreneighboring portions can overlap one another. For example, the analysiswindow can be moved between successive positions by a predeterminedamount (e.g., one survey station) that is smaller than a width of theanalysis window (e.g., 10 survey stations).

For each portion of the data (e.g., for each position of the analysiswindow), a tortuosity parameter value can be calculated for the analysiswindow based on two or more survey stations within the analysis window.FIG. 7B schematically illustrates a distance (S1) along the wellborepath between the two survey stations for “analysis window 1” and adistance (L1) in a straight line between the two survey stations for“analysis window 1.” FIG. 7B also schematically illustrates a distance(S2) along the wellbore path between the two survey stations for“analysis window 2” and a distance (L2) in a straight line between thetwo survey station for “analysis window 2.” In certain embodiments, thetwo survey stations can be at respective ends of the analysis window. Incertain embodiments, if the survey station positions are calculated fromthe original survey data (e.g., not from smoothed data), the distance Scan be defined as the sum of the measured depths (MD) between sequentialsurvey stations from a first (e.g., start) survey station to a second(e.g., end) survey station of the analysis window: S=Σ_(j) dMD_(j),where dMD_(j) is the measured depth (along the wellbore) incrementbetween two neighboring survey stations, with the summation taken overall the increments within the analysis window.

The value of the tortuosity parameter (e.g., T=S/L−1) can be calculatedfor each analysis window, and in certain embodiments, the values of thetortuosity parameter T can be plotted as a function of the measureddepth (MD) to provide a graph of the tortuosity as a function of MD. Forexample, for “analysis window 1,” the tortuosity parameter T will have alow to moderate value since this portion of the wellbore path isrelatively smooth. For “analysis window 2,” the tortuosity parameter Twill have a high value since this portion of the wellbore path hassignificant perturbations relative to the straight line of “analysiswindow 2.”

In certain embodiments, the tortuosity parameter can be decomposed intovarious components. For example, if the distance S is expressed asS=L+dS_(lse)+dS_(sse), where dS_(lse) is the long-scale elongations(e.g., contribution to elongation compared to L from long-scalevariations) of the wellbore path and dS_(sse) is the short-scaleelongations (e.g., contribution to elongation compared to L fromshort-scale variations) of the wellbore path, then the tortuosityparameter T=(S/L)−1 can be expressed as T=dT_(lse)+dT_(sse), wheredT_(lse)=dS_(lse)/L is the long-scale tortuosity of the wellbore pathand dT_(sse)=dS_(sse)/L is the short-scale tortuosity of the wellborepath. The short-scale tortuosity dT_(sse) can be expected to have thegreatest influence on where equipment may be positioned along thewellbore path. In certain embodiments, the tortuosities on variouslength scales can be identified and separated from each other. Forexample,

-   -   the long-scale tortuosity dT_(lse) can be identified using at        least one of the spectral analysis technique and the        displacement technique described above.    -   the short-scale tortuosity dT_(sse) can be derived by        subtracting the long-scale tortuosity dT_(lse) from the total        tortuosity T derived using the path elongation technique.        The short-scale elongation dS_(sse) can also be derived directly        by high-pass spatial filtering of one or more of the parameters        (Inc, Az, N, E, V) as a function of MD and the short-scale        tortuosity dT_(sse) can be derived from short-scale elongation        dS_(sse) using the relation dT_(sse)=dS_(sse)/L.

Display of Tortuosity

Various techniques may be used to display the tortuosity determined byone or more of the above-described techniques in accordance with certainembodiments described herein. For example, a tabular listing of numericvalues can be displayed. For another example, graphical images orstructures can be used to display the tortuosity. Such graphical imagesor structures can include, but are not limited to, graphs of thetortuosity parameter (e.g., T=S/L−1; D_(eff)) versus another parameterof the wellbore (e.g., measured depth); color-coded plots;two-dimensional plots or three-dimensional plots showing how thetransverse displacements restrict the physical space available to adevice within the wellbore (e.g., shown directly as renderings ofphysical objects; shown by color coding); three-dimensional physicalmodel (e.g., manufactured by 3D printing) of the portion of the wellboreor casing section of interest (e.g., a reduced scale model, which can becompact or hollow) along with a physical model (e.g., manufactured by 3Dprinting) of the device to be inserted within the wellbore (e.g., areduced scale model of the device with the same scale as the reducedscale model of the portion of the wellbore). In certain embodiments, thegraphical images or structures can also include other wellbore data(e.g., drilling procedure data, data from logs or logging-while-drillingsurveys). For example, the graphical images or structures can includedata regarding the tortuosity (e.g., path elongation) parameter or thevarying (e.g., reduced) diameter of the wellbore (e.g., shown as a graphor using color coding) with traditional log displays.

In certain embodiments, a threshold value of tortuosity can bepredetermined and in a display showing the wellbore path, the portionsof the wellbore path having a tortuosity less than the threshold valuecan be shown in a different manner than are the portions of the wellborepath having a tortuosity greater than the threshold value. For example,the portions of the wellbore path having a tortuosity less than thethreshold value can be labeled as “low” and the portions of the wellborepath having a tortuosity greater than the threshold value can be labeledas “high.” For another example, the portions of the wellbore path havinga tortuosity less than the threshold value can be shown using a firstcolor and the portions of the wellbore path having a tortuosity greaterthan the threshold value can be shown using a second color differentfrom the first color. In certain embodiments, the portions of thewellbore path are shown with a color coding that corresponds to theamount of tortuosity or the amount of diameter reduction of the portionof the wellbore path. In certain embodiments, an appropriate label canbe generated (e.g., automatically) and displayed with the wellbore pathdata to denote portions of the wellbore path having features orattributes of interest.

FIGS. 8A-8C, 9, and 10 schematically illustrate example displays of thetortuosity determined by one or more of the above-described techniquesin accordance with certain embodiments described herein. Other displayformats may be used to facilitate communicating the tortuosity of thewellbore. In FIG. 8A, the various displacements resulting from themethod 200 are plotted as points in the x-y plane (e.g., with the x-axiscorresponding to a lateral direction and the y-axis corresponding to ahigh side direction). Displacements having magnitudes within apredetermined area (e.g., within the area bounded by the dashed line inFIG. 8A) can be considered to be in a low displacement region of thedisplay (e.g., denoting portions of the wellbore path having lowtortuosity) and displacements having magnitudes outside thepredetermined area can be considered to be in a high displacement regionof the display (e.g., denoting portions of the wellbore path having hightortuosity). Such displays can be advantageously used to reveal largedisplacement magnitudes or trends in the offset direction of thedisplacements. In FIG. 8B, the various displacements are plottedsequentially (e.g., from a start station sequentially to an end station)in the x-y plane (e.g., with the x-axis corresponding to a lateraldirection and the y-axis corresponding to a high side direction). Suchdisplays can be advantageously used to reveal wellbore spiraling orother conditions in which the displacements exhibit a certain trend orvary systematically in direction along the wellbore. In FIG. 8C, thevarious displacements are used to overlay circles representing thecasing or wellbore wall cross-sections in the x-y plane, showing how thedisplacement varies with measured depth (MD). In FIG. 9, the casing orwellbore wall cross-sections are shown in a three-dimensional rendering.In displays such as those of FIGS. 8C and 9, the displacements may bescaled up with respect to the casing or wellbore cross-sectiondimensions, in order to show the tortuosity more clearly. In certainembodiments, displays similar to those of FIGS. 8A-8C and 9 may be usedto show the magnitude of the tortuosity parameter.

In FIG. 10, the tortuosity (e.g., path elongation) parameter T isplotted as a function of the measured depth (MD). Similar graphs may bedisplayed to show the tortuosity based on Inc data alone, on Az dataalone, on any combination of Inc, Az, N, E, or V data, or data separatedinto large-scale and small-scale variations.

FIGS. 11A and 11B show example three-dimensional renderings of thetransverse displacement measured along a portion of a wellbore inaccordance with certain embodiments described herein. FIG. 11Acorresponds to a gyroscopic survey taken with survey stations atone-foot intervals, while FIG. 11B corresponds to ameasurement-while-drilling (MWD) survey taken with survey stations atapproximately 30-100 feet intervals. The portion of the wellbore inFIGS. 11A and 11B has a measured depth between 7000 feet and 8000 feet.The casing diameters and transverse displacements are scaled up in FIGS.11A and 11B for illustration purposes. The transverse displacement at asurvey station in the wellbore is the deviation of the survey stationfrom the best straight line fit around the vicinity of the surveystation. A small deviation indicates a smooth well path at the surveystation, while a large deviation indicates a high well path variation.As shown in FIGS. 11A and 11B, the color or shading of a specificportion of the wellbore can be indicative of the magnitude of thetransverse displacement at the specific portion of the wellbore.

FIGS. 12A and 12B show example highside, lateral, and total transversedisplacements as a function of measured depth of a portion of a wellborein accordance with certain embodiments described herein. FIG. 12Acorresponds to a gyroscopic survey taken with survey stations atone-foot intervals, while FIG. 12B corresponds to ameasurement-while-drilling (MWD) survey taken with survey stations atapproximately 30-100 feet intervals. The transverse displacement isdefined as described above with regard to FIGS. 11A and 11B. The totaltransverse displacement comprises a highside component and a lateralcomponent. The polarities of these components denote their direction.

FIGS. 13A and 13B show an example tortuosity of the wellbore as afunction of measured depth in accordance with certain embodimentsdescribed herein. FIG. 13A corresponds to a gyroscopic survey taken withsurvey stations at one-foot intervals, while FIG. 13B corresponds to ameasurement-while-drilling (MWD) survey taken with survey stations atapproximately 30-100 feet intervals. The tortuosity at a point in thewellbore in FIGS. 13A and 13B is defined as the ratio of the lengthalong a section of the wellbore around the vicinity of the point to thelength of a straight line joining the ends of the section, reduced byone (e.g., T=S/L−1). The length of the section is selected to beapproximately equal to the length of the device to be placed in thewellbore. A high tortuosity signifies a large well path variation, and atortuosity of zero means that the well path around the point fits astraight line. The tortuosity can be separated into small-scale andlarge-scale variations. In FIGS. 13A and 13B, the tortuosity computedfrom the raw data is the total tortuosity. The tortuosity derived fromthe smoothened data is a function of the large-scale variation. Thedifference between the total and the large-scale tortuosity is a measureof the small-scale (e.g., high spatial frequency) well path variation.

FIGS. 14A and 14B show example plots of the maximum outer diameter of amodel device 90 feet long that can be placed at a specific measureddepth along the wellbore in accordance with certain embodimentsdescribed herein. FIG. 14A corresponds to a gyroscopic survey taken withsurvey stations at one-foot intervals, while FIG. 14B corresponds to ameasurement-while-drilling (MWD) survey taken with survey stations atapproximately 30-100 feet intervals. The maximum outer diameter will below at depths where the well path variation is high, and can be nohigher than the casing inner diameter of the wellbore (e.g., 6.04inches).

Conditional language used herein, such as, among others, “can,” “could,”“might,” “may,” “e.g.,” and the like, unless specifically statedotherwise, or otherwise understood within the context as used, isgenerally intended to convey that certain embodiments include, whileother embodiments do not include, certain features, elements and/orstates. Thus, such conditional language is not generally intended toimply that features, elements and/or states are in any way required forone or more embodiments or that one or more embodiments necessarilyinclude logic for deciding, with or without author input or prompting,whether these features, elements and/or states are included or are to beperformed in any particular embodiment.

Depending on the embodiment, certain acts, events, or functions of anyof the methods described herein can be performed in a differentsequence, can be added, merged, or left out completely (e.g., not alldescribed acts or events are necessary for the practice of the method).Moreover, in certain embodiments, acts or events can be performedconcurrently, e.g., through multi-threaded processing, interruptprocessing, or multiple processors or processor cores, rather thansequentially.

The various illustrative logical blocks, modules, circuits, andalgorithm steps described in connection with the embodiments disclosedherein can be implemented as electronic hardware, computer software, orcombinations of both. To clearly illustrate this interchangeability ofhardware and software, various illustrative components, blocks, modules,circuits, and steps have been described above generally in terms oftheir functionality. Whether such functionality is implemented ashardware or software depends upon the particular application and designconstraints imposed on the overall system. The described functionalitycan be implemented in varying ways for each particular application, butsuch implementation decisions should not be interpreted as causing adeparture from the scope of the disclosure.

The various illustrative logical blocks, modules, and circuits describedin connection with the embodiments disclosed herein can be implementedor performed with a processor, a digital signal processor (DSP), anapplication specific integrated circuit (ASIC), a field programmablegate array (FPGA) or other programmable logic device, discrete gate ortransistor logic, discrete hardware components, or any combinationthereof designed to perform the functions described herein. A processorcan be a microprocessor, but in the alternative, the processor can beany conventional processor, controller, microcontroller, or statemachine. A processor can also be implemented as a combination ofcomputing devices, e.g., a combination of a DSP and a microprocessor, aplurality of microprocessors, one or more microprocessors in conjunctionwith a DSP core, or any other such configuration.

The blocks of the methods and algorithms described in connection withthe embodiments disclosed herein can be embodied directly in hardware,in a software module executed by a processor, or in a combination of thetwo. A software module can reside in RAM memory, flash memory, ROMmemory, EPROM memory, EEPROM memory, registers, a hard disk, a removabledisk, a CD-ROM, or any other form of computer-readable storage mediumknown in the art. An exemplary tangible, computer-readable storagemedium is coupled to a processor such that the processor can readinformation from, and write information to, the storage medium. In thealternative, the storage medium can be integral to the processor. Theprocessor and the storage medium can reside in an ASIC. The ASIC canreside in a user terminal. In the alternative, the processor and thestorage medium can reside as discrete components in a user terminal.

Although described above in connection with particular embodiments, itshould be understood that the descriptions of the embodiments areillustrative of the invention and are not intended to be limiting.Various modifications and applications may occur to those skilled in theart without departing from the true spirit and scope of the invention asdefined in the appended claims.

What is claimed is:
 1. A method, comprising: receiving survey datacorresponding to a plurality of survey stations of a wellbore survey ofa wellbore path; determining a plurality of curved reference lines forthe wellbore path based on the received survey data; and determining aplurality of displacements of the wellbore path from the plurality ofreference lines.
 2. The method of claim 1, wherein the plurality ofcurved reference lines are within a plurality of analysis windows, andwherein each analysis window denotes a corresponding portion of thesurvey data.
 3. The method of claim 2, wherein determining the pluralityof curved reference lines comprises determining a respective curvedreference line within a respective analysis window based on two or moresurvey stations within the respective analysis window.
 4. The method ofclaim 2, wherein determining the plurality of curved reference linescomprises determining a respective curved reference line within arespective analysis window based on a weighted best fit of positions ofsurvey stations within the respective analysis window to a curved line.5. The method of claim 2, wherein determining the plurality of curvedreference lines comprises determining a respective curved reference linewithin a respective analysis window based on a spatial low-passfiltering of data regarding positions of the wellbore path at surveystations within the respective analysis window, data regarding thenorth, east, and vertical coordinates of the wellbore path at surveystations within the respective analysis window, or combinations thereof.6. The method of claim 2, wherein determining the plurality of curvedreference lines comprises iteratively updating a respective curvedreference line within a respective analysis window based on deviationsof an initial reference line from the wellbore path.
 7. The method ofclaim 2, wherein determining the plurality of displacements comprises,for a respective analysis window, determining a displacement of thewellbore path at one or more predetermined positions within therespective analysis window.
 8. The method of claim 1, whereindetermining the plurality of reference lines of the wellbore pathcomprises determining a first reference line which extends from a surveystation to a subsequent survey station.
 9. The method of claim 8,wherein determining the plurality of displacements comprises:determining a first maximum displacement of the wellbore path from thefirst reference line; and denoting a location of the first maximumdisplacement as being a first contact point.
 10. The method of claim 9,wherein determining the plurality of reference lines for the wellborepath comprises determining a second reference line which extends fromthe first contact point to a subsequent survey station.
 11. The methodof claim 10, wherein determining the plurality of displacementscomprises: determining a second maximum displacement of the wellborepath from the second reference line; and denoting a location of thesecond maximum displacement as being a second contact point.
 12. Themethod of claim 11, wherein a location of at least one of the firstcontact point and the second contact point is adjusted using anadjustment reference line defined using other contact points.
 13. Themethod of claim 11, further comprising: quantifying a degree of bend ata respective contact point as a normalized displacement equal to amaximum displacement of the respective contact point divided by a lengthof a straight reference line extending between a previous contact pointand a subsequent contact point; setting a threshold level and performinga comparison of at least a portion of the normalized displacements tothe threshold level; and using the comparison to determine potentiallocations along the wellbore path for one or more rod guides to beplaced.
 14. The method of claim 1, wherein the received survey datacomprises gyroscopic data, data from magnetic instruments, orcombinations thereof
 15. A method, comprising: receiving survey datacorresponding to a plurality of survey stations of a wellbore survey ofa wellbore path; and determining tortuosity for the wellbore path withina plurality of analysis windows based on the received survey data andbased on a maximum device length (L_(max)) for a respective analysiswindow, wherein the L_(max) comprises a maximum allowed length of amodel tubular device that can be placed at, or passed through, a portionof a wellbore defined by the respective analysis window.
 16. The methodof claim 15, wherein the maximum allowed length of the model tubulardevice is determined based on a predetermined limit for transversalforces experienced by the model tubular device, a predetermined limitfor transversal moments experienced by the model tubular device, orcombinations thereof.
 17. The method of claim 15, determining thetortuosity further comprises determining the tortuosity for the wellborepath based on an effective inner diameter (D_(eff)) for the respectiveanalysis window, wherein the D_(eff) comprises a maximum width of anouter periphery of the model tubular device having the L_(max) that canbe placed at, or passed through, the portion of the wellbore defined bythe respective analysis window.
 18. A method, comprising: receivingsurvey data corresponding to a plurality of survey stations of awellbore survey of a wellbore path; and determining tortuosity for thewellbore path within a plurality of analysis windows based on thereceived survey data and based on an effective inner diameter (D_(eff))for a respective analysis window, wherein the D_(eff) comprises amaximum width of an outer periphery of a model device with a specifiedlength that can be placed at, or passed through, a portion of a wellboredefined by the respective analysis window and configured to withstand aspecified amount of bending.
 19. The method of claim 18, wherein themaximum width of the outer periphery of the model device comprises amaximum allowed outer diameter of the model device with the specifiedlength that can be placed at, or passed through, the portion of thewellbore defined by the respective analysis window.
 20. The method ofclaim 18, wherein whether the model device can be placed at, or passedthrough, the portion of the wellbore defined by the respective analysiswindow is determined based on an amount of transversal forces (F) thatthe model device would experience while the model device is within theportion of the wellbore, an amount of transversal moments (M) that themodel device would experience while the model device is within theportion of the wellbore, or combinations thereof.